# Solving non-monotone equilibrium problems via a DIRECT-type approach

arXiv: https://arxiv.org/abs/2002.12198 · HTML: https://mlsanity.com/paper/2002.12198/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [Learning equilibria with personalized incentives in a class of nonmonotone games](https://mlsanity.com/paper/2111.03854/) (2021)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)

## Abstract (arXiv)

A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the textttDIRECT algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.